Decomposition of tensor products of modular irreducible representations for SL3: the p ? 5 case

We study the structure of the indecomposable direct summands of tensor products of two restricted rational simple modules for the algebraic group SL3(K), where K is an algebraically closed field of characteristic p ? 5. We also give a characteristic-free algorithm for the decomposition of such a tensor product into indecomposable direct summands. The p < 5 case was studied in the authors’ earlier paper [4]. We find that for characteristics p ? 5 all the indecomposable summands are rigid, in contrast to the characteristic 3 case.